Mathematics, 01.06.2021 03:40 TrueKing184

Two companies modeled their profits for one yeor Which stotement describes the relationship between the profits, predicted by the models of the two companies?

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Answer from: SoccerdudeDylan

The question is incomplete. The complete question is :

Two companies modeled their profits for one year.

Company A used the function P(t)=1.8(1.4)^t to represent its monthly profit, P(t), in hundreds of dollars, after t months, where 0 < t ≤ 12. Company B used the data in the table to write a linear model to represent its monthly profits.

Which statement describes the relationship between the profits, predicted be the models, of the two companies?

Solution :

For one year, the two companies A and B modeled their profits.

It is given that :

Company A uses function $P(t) = (1.8)(1.4)^t$ in order to represent the monthly profit of the company in hundreds of dollars after a time .

But the company B uses the data in the table in order to write the linear model to represent their monthly income.

We know the linear function is given by :

$P(t)=mt+c$

Here, m = slope of line

c = y-intercept

According to the data from the table , we see that the two points (3.5) and (4.10) lies on the line so that the slope of the line is represented by :

$\frac{y-y'}{x-x'}=\frac{10-5}{4-3}=5$

The point (3.5) passes through the given line.

∴ $5=5(3)+c$

$5=15+c$

$c=5-15$

$c=-10$

Therefore, the function will be $P(t) = 5t-10$

So, at t=4 ,

the profit of the company A is $P(4)=(1.8)(1.4)^4$

= 6.91

the profit of the company A is $P(4)=5(4)-10$

= 20 - 10

= 10

Therefore, t=4 , the profit of the company B is more than the profit of company A.

Now at t=12 ,

Profit of company A is $P(12) =(1.8)(1.4)^{12}$

= 102.05

Profit of company B is P(12)=5(12)-10

$=66-10$

= 56

Therefore, the profit of company A is more that that of company B at the end of the year one.

Thus, company B had a greater profit for the fourth month and ended the year with the greater monthly profits than company A.

Option (B) is the correct answer.

Two companies modeled their profits for one yeor Which stotement describes the relationship between

Answer from: Quest

3; 9 is 8 to -4

step-by-step explanation:

Answer from: Quest

is should be y = 5x

step-by-step explanation:

correct me if im wrong

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